# Math 222H: Differential Equations - HonorsSpring 2018 Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

## Course Information

Course Description: Topics enhance those of Math 222 and concepts are studied in detail. Emphasizes science and engineering applications. Effective From: Fall 2012.

Number of Credits: 4

Prerequisites: Math 112H with a grade of B or better or Math 112 with a grade of A.

Course-Section and Instructors

Course-Section Instructor
Math 222-H02 Professor J. Bechtold

Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails

Required Textbook:

 Title Elementary Differential Equations and Boundary Value Problems Author Boyce and DiPrima Edition 10th Publisher John Wiley & Sons, Inc. ISBN # 978-0470458310

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 2, 2018. It will be strictly enforced.

## Course Goals

### Course Objectives

• Students should (a) learn elementary analytical solution techniques for the solution of ordinary differential equations (ODEs), and (b) understand the solution structure of linear ODEs in terms of independent homogeneous solutions and non-homogeneous solutions.
• Students should (a) understand by exposure to examples how systems and phenomena from science and engineering can be modeled by ODEs, and (b) how solution of such a model can be used to analyze or predict a system’s behavior. A key example is the damped, forced, simple harmonic oscillator.
• Students should understand the role of initial value problems for ODEs in examples from science engineering, and should be introduced to the role of two-point boundary value problems and Fourier series.
• Students should understand an elementary method for the numerical solution of ODEs and have some familiarity with the solution of ODEs using MATLAB.

### Course Outcomes

• Students have improved problem-solving skills, including knowledge of techniques for the solution of ODEs.
• Students have an understanding of the importance of differential equations in the sciences and engineering.
• Students are prepared for further study in science, technology, engineering, and mathematics.

Course Assessment: The assessment of objectives is achieved through homework assignments and common examinations with common grading. Homework assignments chosen from the text are listed below. Students are required to work through these problems after each lecture in order to gain a better understanding of the course material. Seven or eight additional problem sets will be assigned during the course of the semester. These are an extremely important component of the homework grade.

## Policies

DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.

Grading Policy: The final grade in this course will be determined as follows:

 Homework, Quizzes, and MATLAB 17% Common Midterm Exam I 17% Common Midterm Exam II 17% Common MIdterm Exam III 17% Final Exam 32%

Your final letter grade will be based on the following tentative curve.

 A 85 - 100 C 65 - 69 B+ 80 - 84 D 60 - 64 B 75 - 79 F 0 - 59 C+ 70 - 74

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Exams: There will be three midterm exams held during the semester and one comprehensive final exam. Exams are held on the following days:

 Common Midterm Exam I February 14, 2018 Common Midterm Exam II March 7, 2018 Common Midterm Exam III April 18, 2018 Final Exam May 4 - 10, 2018

The time of the midterm exams is 4:15 - 5:40PM for daytime students and 5:45 - 7:10PM for evening students. The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2018 Hours)

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

# Course Outline

Week Section Topic Lecture HW Assignment
1
1.1 Some Basic Models; Direction Fields  1 8, 10, 11, 17, 18, 23
1.3 Classification of Differential Equations 2 1, 2, 5, 6, 8, 11
2
2.1 Linear Equations; Integrating Factors 3 6(c), 9(c), 17, 19, 22(b, c)
2.2 Separable Equations 4 3, 6, 8, 9, 12, 16
2.3 Modeling with First Order Equations 5 2, 4, 7, 9
3
2.3 Modeling, Continued 6 16, 18(a)
2.7 Numerical Approximation;  7 2
Euler’s Method
3.1 Homogeneous Equations with  8 3, 6, 8, 10, 13, 17,
Constant Coefficients 20, 22, 23
4
3.2 Solutions of Linear Homogeneous Equations; the Wronskian 9 2, 5, 6, 8, 12, 18
Review for Exam 1 10
Common Exam 1, Wednesday, February 14, 2018
3.2 The Wronskian, Continued 11 22, 24, 25, 26, 31
5
3.3 Complex Roots of the Characteristic Equation 12 2, 3, 5, 7, 11, 17, 21, 27
3.4 Repeated Roots; Reduction of Order 13 1, 6, 9, 11, 14, 16, 26, 28, 30
3.5 Nonhomogeneous Equations;  14 3, 5, 9, 11, 17, 19,
Undetermined Coefficients
6 3.5 Undetermined Coefficients, Continued 15 22(a), 23(a), 25(a), 28(a)
3.6 Variation of Parameters 16 3, 7, 8, 9, 12, 13, 15, 19
3.7 Mechanical and Electrical  17 2, 3, 5, 7, 11, 12,
Vibrations
7 3.7 Vibrations, Continued 18 14, 16, 17, 18, 20
3.8 Forced Vibrations 19 2, 6, 9, 12
5.1 Review of Power Series 20 18, 20, 21, 23
8 5.2 Series Solutions of Second Order Linear ODEs with Non-Constant Coefficients; Solution Near an Ordinary Point   21 2(a, b), 4(a, b)
Review for Exam 2 22
Common Exam 2, Wednesday, March 7, 2018
5.2 Series Solutions Near an Ordinary Point, Continued 23 7(a, b), 12(a, b)
Spring Recess:  Sunday, March 11 to Sunday, March 18, 2018
9 5.4 Euler’s Equation; Regular Singular Points 24 1, 3, 4, 8, 17, 20, 22
6.1
& 6.2
Definition of the Laplace Transform
& Solution of Initial Value Problems
25 6.1: 3, 4, 6, 9, 13, 15, 21,
6.2 Initial Value Problems, Continued 26 6.2; 1, 2, 3, 5, 7, 8, 13,
10 6.3 Step Functions 27 2, 4, 10, 11, 15, 17, 20, 21, 23
6.4 ODEs with Discontinuous Forcing Functions 28 2, 3, 5, 7, 9, 11
6.5 Impulse Functions  29 1, 2, 5, 6, 9
11 6.6 The Convolution Integral  30 4, 5, 6
6.6 Convolution, Continued 31 8, 9, 10, 14, 18
7.1 Systems of First Order
Linear ODEs
32 2, 4, 5, 7(a, b)
12 Review of Linear Algebraic Equations, Eigenvalues and Eigenvectors (2x2) 33 7.3: 16, 17, 18, 19
7.5 Homogeneous Linear Systems with Constant Coefficients 34 2(a), 4(a), 7(a), 15, 16
7.6 Complex Eigenvalues  35 2(a), 6(a), 10
13 7.6 Complex Eigenvalues, Continued  36 13, 17, 28
Review for Exam 3 37
Common Exam 3, Wednesday, April 18, 2018
10.1 Two-Point Boundary Value Problems 38 1, 3, 5, 10, 14, 15, 18
14 10.2 Fourier Series 39 1, 5, 6, 7, 13, 15, 16
10.2 Fourier Series, Continued  40 19(a, b), 20(a, b), 22(a, b)
10.4 Even and Odd Functions  41 2, 3, 4, 7, 9, 15, 16, 21, 23(a, b), 27(a, b)
15 Review for Final Exam  42

Updated by Professor J. Bechtold - 1/15/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018